2A+Arithmetic+Sequences

Shareesa Bollers the range for arithmetic sequences will consist of whole numbers. Sometimes true 1, 3, 5, 7, 9, 11, 13 1, 2.5, 4, 5.5, 7, 8.5, 10

Arithmetic sequences are recursive Always True 1, 2, 3, 4, 5, 6, 7, 8

When given the graph of an arithmetic sequence, which contains two points, you should be able to determine the initial value and the common difference. a. Always True b. 2, 6, 10, 14, 18, 22

In arithmetic sequences you add or subtract by a common number. The number added or subtracted in the sequence is called the Common Difference. The values of an arithmetic sequence have a linear relationship.

The graph below shows the relationship of points on with an positive arithmetic generator.



source: www.cpm.org

Scott Thayres

At least two terms are needed in order to write a formula for an arithmetic sequence. If you have a number and the generator is +3, but you don't know and you can't figure it out with just one number. If you had two numbers and the common difference is 3, then you can figure out what the generator is.

When given the graph of an arithmetic sequence, which contains two points, you should be able to determine the initial value and the common difference. look at it as an equation y=mx+b. y= the value, m= the generator and b equals the starting number. ???????????????????????

The domain for arithmetic sequences are counting numbers including zero. If you have two points at (5,6) and (-1,7) then the domain would be -1 ->6. Both negative and postive are being used in domain and since zero is in between the two, it has to be used when having a domain heading from negative to positive and vis versa. (spelling)

The range for arithmetic sequences will consist of whole numbers. You can add .5 and other deciamals to get whole numbers.???????????????

The graphs of an arithmetic sequence are continuous. The sequence has no end which means it goes on continuesly as well as the graph

The staircase of a quadratic sequence is an arithmetic sequence. Each common difference is different so as the points are farther and farther, the number used as the generator must be getting higher.

Charles Williams John Derry

Every number always has an [|additive inverse] because both negative and positive numbers can be added to its opposite to make zero. Like 2 + -2 is equal to zero. Since additive means he number will be added this will always be true with any number. For Example The additive inverse of 7 is −7, because 7 + (−7) = 0

Sometimes true Arithmetic sequences can have a generator of a whole number or a mixed number. For example: t(n)=1+1.5n 1,2.5,4,5.5,7,8.5,10
 * Arithmetic sequences will consist of whole numbers.**

t(n)=1+1n 1,2,3,4,5,6


 * Sophia Moreno**

o Always True
 * 1.** Arithmetic Sequences are recursive.

The purpose of an arithmetic sequence is that the same number is added or subtracted over and over again. It follows the same rule consecutively.

An ARITHMETIC SEQUENCE is a sequence with an addition (or subtraction) generator. (Check pg. 51)

1, 4, 7, 10 +3 +3 +3

o Sometimes True
 * 2.** At least two terms are needed in order to write a formula for an arithmetic sequence.

I think it would depend on if you knew it was an arithmetic sequence or not. Suppose the sequence was ‘12, 6, ,’ you could say that the rule is -6, or x/2.

o Always True
 * 3.** The domain for arithmetic sequences are counting numbers including zero.

Yes, because the domain is the x value on a graph and represents the number in the sequence, not its value, but what place it takes. (The 1st number in the sequence or the 5th number in the sequence.)

o Never True
 * 4.** The graphs of an arithmetic sequence are continuous.

The graph shows individual points. They are not connected because the x values can only be whole numbers.

o Sometimes True
 * 5.** The range for arithmetic sequences will consist of whole numbers.

{2.5, 4.5, 6.5} is a possible range (2, 4, 6) is a possible range

o Always True
 * 6.** If you are given the algebraic formula for an arithmetic sequence, then you should be able to determine the initial value and the common difference of the sequence.

Y = i + dx

Y = y coordinate X = x coordinate (place of number in sequence) i = initial value d = common difference

Example: rule = +2 X 0 1 2 3 Y 2 4 6 8

o Sometimes True
 * 7.** In order to write the formula for an arithmetic sequence, you need to be given the initial value.

?

o Always True check the y intercept and the y axis staircases
 * 8.** When given the graph of an arithmetic sequence, which contains two points, you should be able to determine the initial value and the common difference.


 * Kimberly Bush**

1: Always True -It has a recursive pattern

2: Sometimes True -If the pattern never changes then you should be able to know the next term -Sometimes you might need another term because it might be a different pattern //-Ex. 2,4-// -The pattern could be +2 or x2

3: Always True //-Ex.-// __n}{t(n)__ 0}{2 1}{4 2}{6

4: Always True -It can increase and decrease

5: Sometimes True -The range could be a whole number or a fraction/decimal

6: Always True //-Ex.-// Algebraic Formula: t(n)=2n+2

7: Sometimes True -It depends on the information given //-Ex.-// __n}{t(n)__ 0}{2 1}{4

or __n}{t(n)__ 0}{2 1}{4 2}{8

The formula above would not work for the second chart

8: Sometimes True -Look to problem 7

Aimee Leong

1. Arithmetic Sequences are recursive. -Always True In an **arithmetic Sequences** the difference between sequential terms is constant. Each term of an arithmetic sequence can be generated by adding the common difference to the previous term.
 * Recursive** is relating to or involving the repeated application of a rule, definition, or procedure to successive results.

2. At least two terms are needed in order to write a formula for an arithmetic sequence. -Sometimes True In an **arithmetic Sequences** the difference between sequential terms is constant. Each term of an arithmetic sequence can be generated by adding the common difference to the previous term. If the sequential terms are constant than you'll be able to figure out what the next term is. But sometimes the sequence might change. For example: 2, 4, 6 the rule would be: +2 or 2n

3. The domain for arithmetic sequences are counting numbers including zero. -Always True For example:
 * = **n** ||= **t(n)** ||
 * = 0 ||= 2 ||
 * = 1 ||= 4 ||
 * = 2 ||= 6 ||
 * = 3 ||= 8 ||

5. The range for arithmetic sequences will consist of whole numbers. -Sometimes True The range could be a whole number or a fraction or decimal.

6. If you are given the algebraic formula for an arithmetic sequence, then you should be able to determine the initial value and the common difference of the sequence. -Always True

7. In order to write the formula for an arithmetic sequence, you need to be given the initial value. -Sometimes True I think because its based off on what information is given.

 Eddie Abbott

 The graphs of a arithmetic sequence are continuous - never true The X values must be whole numbers for the graph to connect.

 In order to write the formula for an arithmetic sequence, you need to be given the initial value. - sometimes true Lets say that instead of the 1st number you are given the 3rd, 4th, and 5th. you can still find out the sequence because it would be the same as having the 1st, 2nd, and 3rd number.

 Arithmetic sequences are recursive.- always true they are recursive because there is a constant change in the number outcome.

 At least two terms are needed in order to write a formula for an arithmetic sequence.- sometimes true at least two terms are needed because you cannot figure out the sequence just from one number.

 The staircase of a quadratic formula is an arithmetic sequence.- always true The graph goes by a certain number each time.

Lenea Harris 4. Arithmetic sequences are recursive. Always True Sometimes True Never True

Answer: Always True

Examples: An arithmetic sequence is a sequence that has a common difference between the terms.

2,5,8,11

Common difference is 3. The difference is repeated. Collaborators: none

9. In order to write an arithmetic sequence you need to be given the initial value. Always True Sometimes True Never True

Answer: Sometimes True

Examples: Initial Value: 6 Constant: 2

6, 8, 10, 12, 14

You can find the initial value with enough terms. ?, 8, 10, 12, 14 Initial value is 6. Collaborators: none

12. At least two terms are needed to write a formula for an arithmetic sequence. Always True Sometimes True Never True

Answer: Sometimes True

1,2…. T(n)= n+1

1,2,3,4,5

t(n)= n+1

Collaborators: none

14. The range for arithmetic sequences will consist of whole numbers. Always True Sometimes True Never True

Answer: Sometimes True

Examples:

Range: (2,2.5,3,)

Collaborators: none

19. The domain for arithmetic sequences are counting numbers including zero. Always True Sometimes True Never True

Answer: Always True

Examples: Domain: ( -2,-1,0,1,2) Collaborators: none.